tan20°+tan25°+tan20°tan25°=?

প্রশ্ন: \( \tan 20^\circ + \tan 25^\circ + \tan 20^\circ \tan 25^\circ = ? \)

আমরা জানি, \( \tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \).

ধরি, \( A = 20^\circ \) এবং \( B = 25^\circ \).

তাহলে, \( \tan(20^\circ + 25^\circ) = \tan(45^\circ) = 1 \).

অতএব, \( \frac{\tan 20^\circ + \tan 25^\circ}{1 - \tan 20^\circ \tan 25^\circ} = 1 \).

সুতরাং, \( \tan 20^\circ + \tan 25^\circ = 1 - \tan 20^\circ \tan 25^\circ \).

এখন, \( \tan 20^\circ + \tan 25^\circ + \tan 20^\circ \tan 25^\circ = 1 \).

সুতরাং, উত্তর: \( 1 \).

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